Answer:
The percent decrease in the price of shirt is 27.78%
Step-by-step explanation:
The percent decrease is the decrease in the price of a product or good.
Given
Original Price = $45
Decreased price = $32.50
Percentage decrease is calculated by using the formula
[tex]Percentage\ decrease = \frac{decrease}{Original\ price} *100\\[/tex]
And the decrease is calculated as:
[tex]Decrease = Original\ price - Reduced\ price[/tex]
So,
[tex]Decrease = 45-32.50 = 12.5[/tex]
Putting the values in the formula for percent decrease
[tex]Percent\ decrease = \frac{12.50}{45} *100\\=0.2777..*100\\= 27.77..[/tex]
Rounding off to nearest hundredth: 27.78%
Hence
The percent decrease in the price of shirt is 27.78%
Write an equation for the line in the given form.
slope is -5 and (5, 4) is on the line; standard form
Answer:
5x+y=29
Step-by-step explanation:
You use the information that is given and convert it into point-slope form y-y1=m(x-x1) like so. y-4= -5(x-5). Then you solve for y and you get y= -5x+29 which is slope intercept form (y=mx+b). Then you transform it into Standard form (ax+by=c) so all you do is add 5 on both sides and you get 5x+y=29. Now you have found your solution.
If you can please make my answer the brainliest that would be much appreciated. Thanks!
Sebastián was saving $8.50 each week in order to have enough money for a phone that costs $122. If his father started him off with $25, write an inequality that can be used to determine the minimum number of whole weeks, w, Sebastián will need to save.
Step-by-step explanation:
122 - 25
97
y= 8.5x + 25
97/8.50 <
11.4 --> 12
x < 12
Answer:
25 + 8.50w ≥ 122
Step-by-step explanation:
Given that:
Amount saved per week = $8.50
Cost of phone = $122
Starting amount = $25
Minimum Number of whole weeks (w) Sébastien will need to save :
Starting amount + (weekly saving * number of weeks) ≥ 122
25 + 8.50w ≥ 122
8.50w ≥ 122 - 25
8.50w ≥ 97
w ≥ 97/8.50
w ≥ 11.4117
Number of whole weeks = 12
Mr. Peterson saves $55 each time he gets paid. If Mr. Peterson has saved $220, how many times has he gotten paid?
Answer:
4
Step-by-step explanation:
220 divided by 55 is 4
Answer:
He’s gotten paid 4 times.
Step-by-step explanation:
All you have to do is divide 220 by 55 and you get the answer! :)
If f(x) = 3x2 - 2 and g(x) = 2x + 4, find (f - g)(x).
Answer:
(f - g)(x) = 3x² - 2x - 6
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra
Combining like termsStandard Form: ax² + bx + c = 0Step-by-step explanation:
Step 1: Define
f(x) = 3x² - 2
g(x) = 2x + 4
(f - g)(x) is f(x) - g(x)
Step 2: Find
Substitute: (f - g)(x) = 3x² - 2 - (2x + 4)Distribute -1: (f - g)(x) = 3x² - 2 - 2x - 4Combine like terms: (f - g)(x) = 3x² - 2x - 6A rectangular fence with a positive area has length represented by the expression 3x2+5x-8 and width by 2x2+6x
1. Write expressions in terms of x for the perimeter.
2. Write expressions in terms of x for the area. Give your answers in standard polynomial form and show your work.
3. If the perimeter of the rectangular fence is 16 units, prove, using the quadratic formula, that the solutions to the equation are x=1 and x=-3.2.
4. Using the first solution as x, show work and give the dimensions of the rectangular fence.
5. Using the second solution as x, show work and give the dimensions of the rectangular fence.
6. Explain which dimensions of the fence make sense in the context of the problem.
7. Using the dimensions from #6, what is the area of the rectangular fence?
Answer:
1. [tex]Perimeter = 10x^2+ 22x - 16[/tex]
2. [tex]Area = 6x^4 +28x^3 + 14x^2 - 48x[/tex]
3. [tex]x = 1[/tex] or [tex]x = -3.2[/tex]
4. [tex]Length = 0[/tex] and [tex]Width = 8[/tex]
5. [tex]Length = 6.72[/tex] and [tex]Width = 1.28[/tex]
6. Second Solution
7. [tex]Area = 8.6016[/tex]
Step-by-step explanation:
Given
[tex]Length = 3x^2 + 5x - 8[/tex]
[tex]Width = 2x^2 + 6x[/tex]
Solving (1): The perimeter
Perimeter is calculated as thus:
[tex]Perimeter = 2 * (Length + Width)[/tex]
Substitute values for Length and Width
[tex]Perimeter = 2 * (3x^2 + 5x - 8 + 2x^2 + 6x)[/tex]
Collect Like Terms
[tex]Perimeter = 2 * (3x^2+ 2x^2 + 6x + 5x - 8 )[/tex]
[tex]Perimeter = 2 * (5x^2+ 11x - 8 )[/tex]
Open Bracket
[tex]Perimeter = 10x^2+ 22x - 16[/tex]
Solving (2): The Area:
Area is calculated as thus:
[tex]Area = Length * Width[/tex]
Substitute values for Length and Width
[tex]Area = (3x^2 + 5x - 8) * (2x^2 + 6x)[/tex]
Expand Bracket
[tex]Area = 2x^2(3x^2 + 5x - 8) + 6x(3x^2 + 5x - 8)[/tex]
Open Bracket
[tex]Area = 6x^4 + 10x^3 - 16x^2 + 18x^3 + 30x^2 - 48x[/tex]
Collect Like Terms
[tex]Area = 6x^4 + 10x^3 + 18x^3 - 16x^2 + 30x^2 - 48x[/tex]
[tex]Area = 6x^4 +28x^3 + 14x^2 - 48x[/tex]
Solving (3): If perimeter is 16, show that x = 1 and x = -3.2
In (a) [tex]Perimeter = 10x^2+ 22x - 16[/tex]
Substitute 16 for Perimeter
[tex]16 = 10x^2+ 22x - 16[/tex]
Equate to 0
[tex]10x^2+ 22x - 16 -16=0[/tex]
[tex]10x^2+ 22x - 32=0[/tex]
Expand
[tex]10x^2+ 32x -10x- 32=0[/tex]
Factorize
[tex]x(10x + 32) - 1(10x + 32) = 0[/tex]
[tex](x - 1)(10x + 32) = 0[/tex]
Split
[tex]x - 1 =0[/tex] or [tex]10x + 32 = 0[/tex]
[tex]x = 1[/tex] or [tex]10x = -32[/tex]
[tex]x = 1[/tex] or [tex]x = -32/10[/tex]
[tex]x = 1[/tex] or [tex]x = -3.2[/tex]
Solving (4): Using x = 1; Solve the dimension of the rectangle
We have that:
[tex]Length = 3x^2 + 5x - 8[/tex]
[tex]Width = 2x^2 + 6x[/tex]
Substitute 1 for x in the given parameters
[tex]Length = 3(1)^2 + 5(1) - 8[/tex]
[tex]Length = 3*1 + 5*1 - 8[/tex]
[tex]Length = 3 + 5 - 8[/tex]
[tex]Length = 0[/tex]
[tex]Width = 2(1)^2 + 6(1)[/tex]
[tex]Width = 2*1 + 6*1[/tex]
[tex]Width = 2 + 6[/tex]
[tex]Width = 8[/tex]
Solving (5): Using x = -3.2; Solve the dimension of the rectangle
We have that:
[tex]Length = 3x^2 + 5x - 8[/tex]
[tex]Width = 2x^2 + 6x[/tex]
Substitute -3.2 for x in the given parameters
[tex]Length = 3(-3.2)^2 + 5(-3.2) - 8[/tex]
[tex]Length = 3*10.24 + 5(-3.2) - 8[/tex]
[tex]Length = 30.72 -16 - 8[/tex]
[tex]Length = 6.72[/tex]
[tex]Width = 2(-3.2)^2 + 6(-3.2)[/tex]
[tex]Width = 2*10.24 + 6(-3.2)[/tex]
[tex]Width = 20.48 -19.2[/tex]
[tex]Width = 1.28[/tex]
[tex]Length = 6.72[/tex] and [tex]Width = 1.28[/tex]
Solving (6):
In the first solution of the dimensions in number 4, we have that
[tex]Length = 0[/tex] and [tex]Width = 8[/tex]
This dimension can not be considered because the length of a rectangle can not be 0
In the second solution of the dimensions in number 5, we have that
[tex]Length = 6.72[/tex] and [tex]Width = 1.28[/tex]
This dimension makes more sense because both dimensions are greater than 0
Solving (7): Using (6), determine the Area
In (6), we conclude that
[tex]Length = 6.72[/tex] and [tex]Width = 1.28[/tex]
So, Area is calculated as thus:
[tex]Area = Length * Width[/tex]
[tex]Area = 6.72 * 1.28[/tex]
[tex]Area = 8.6016[/tex]
Ann, Ben, and Cheryl share some money in the ratio 3:7:10. Ben received £650 more than Ann.
Calculate the total amount of money that they shared.
Answer:
Total amount = £ 3250
Step-by-step explanation:
Ann : Ben : Cheryl = 3 : 7 : 10
Money Ann received = 3x
Money Ben received = 7x
Money Cheryl received = 10x
Ben received £650 more than Ann.
7x - 3x = 650
4x = 650
x = 650/4
x = £ 162.50
Money Ann received = 3x = 3 *162.50 = £ 487.50
Money Ben received = 7x = 7 *162.50 = £ 1137.50
Money Cheryl received = 10x = 10* 162.50 = £ 1625
Total amount = 487.50 + 1137.50 + 1625 = £ 3250
Jina and her husband are each starting a saving plan. Jina will initially set aside $650 and then add $135 every month to the savings. The amount A (in dollars) saved this way is given by the function =A+135N650, where N is the number of months she has been saving. Her husband will not set an initial amount aside but will add $585 to the savings every month. The amount B (in dollars) saved using this plan is given by the function =B585N. Let T be total amount (in dollars) saved using both plans combined. Write an equation relating T to N. Simplify your answer as much as possible.
Step-by-step explanation:
If A=650+135N; and B=585N,
then A+B= 650+135N+585N=650+620N
T=720N+650
A function assigns values to each element. An equation relating T to N can be represented by T=650+720N.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The function which tells the amount that is been saved by Jina is given by the function A=650+135N, while the function which tells the amount that will be saved by her husband is B=585N.
Since the total saving amount is represented by T which is the sum of the two functions A and B. Therefore, the function of T can be written as,
[tex]\rm T=A+B\\\\T = (650+135N)+585N\\\\T = 650+135N+585N\\\\T = 650+720N[/tex]
Thus, an equation relating T to N can be represented by T=650+720N.
Learn more about Function:
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What is the value of Negative 5 Superscript 6? –15,625 –30 30 15,625
Answer:
D
Step-by-step explanation:
The value of the expression (-5)⁶ is, 15,625. So option D is correct
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
The expression (-5)⁶
In mathematical terms, this means that the expression
⇒ (-5) x (-5) x (-5) x (-5) x (-5) x (-5)
⇒ 15625
So, the value of the expression (-5)⁶ is 15625.
To know more about Expressions check:
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learning task 1 identify if the if the given equation is a polynomial equation or not
Answer:
In particular, for an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions.
Step-by-step explanation:
factorise 2x^2 - 9x -5
Answer:
(x-5)(2x+1)
Step-by-step explanation:
Its called google XD
what is (9x-10y)-(-8x-8y)?
1. So far, Marta has correctly predicted the winner of 6 out of 13 football games. She wants to know how many consecutive games she would have to predict correctly to raise the percent of correct predictions to 65%. (a) Write an equation to represent this situation. (3 points) (b) Solve the equation. Show all steps. (5 points) (c) Answer the question. How many consecutive games must she predict correctly to raise her percent to 65%? (1 point)
Answer:
[(6 + x) / 13+x] = 0.65
7
Step-by-step explanation:
Given that:
Total number of games = 13
Number of correct prediction = 6
Number of correct predictions needed to raise prediction % to 65%
(Number of correct predictions) / (total number of games) = 0.65
Let x = number of additional consecutive correct predictions
[(6 + x) / 13+x] = 0.65
Where x = number of consecutive predictions required
6 + x = (13 + x) * 0.65
6 + x = 8.45 + 0.65x
x - 0.65x = 8.45 - 6
0.35x = 2.45
x = 2.45 / 0.35
x = 7
7 consecutive correct predictions
Name some examples of scale factors that are less than 1. What effect does a scale factor less than 1 have on the dimensions of the image being scaled?
Answer:
0.1 0.001 0.0001
Step-by-step explanation:
Classify the following triangle. Check all that apply.
During his vacation, Dalyn rents a small boat from a rental service that charges a flat fee of $40 plus $20 per hour (including taxes).
The total charge comes to $120. Which equation can be used to calculate the number of hours, a, that Dalyn rents the boat?
Answer:
4 hours
Step-by-step explanation:
We can calculate this using the y=mx+c formula
y=total charge
m=per hour
x = (a) no. of hours
c= flat fee
y=20x+40
120=20x+40
We then solve like a normal equation
120-40=20x+40-40
80/20=20x/20
x=a
a=4
∴ Dalyn rents the boat for 4 hours
HELP 30 Points ANy wrong/bad answers will be deleted by one of my moderator friends.
Hope this helps?
Please mark my answer as brainliest?
what is an eqution for a slope of 2 and a y intercept of 5
Answer:
y=2x+5
Step-by-step explanation:
PLEASE URGENT (ALGEBRA)
Find the number of calories in a honeydew and a cantaloupe
(1.) A honeydew has 20 more calories than a cantaloupe
(2.) Six honeydew and 3 cantaloupes have 750 calories
Answer:
1) A honeydew has 20 more calories than a cantaloupe
When x = 1/2, what is the value of 8x-3/x ?
Please answer this giving brainliest and 20 points. If you say something weird i will make sure you get banned.
Answer:
C. The value of a is the number that the x-values are multiplied by to get to the corresponding y-values. So, a = 3.
Step-by-step explanation:
Given the points (5, 15) and (-5, -15) are plotted using the equation y = a•x, this shows a proportional relationship between y and x.
Thus using any of the points, say (5, 15), x = 5, and y = 15, thus:
a = y/x = 15/5
a = 3
Therefore, the value of a, which is 3, is the number that the x-values, 5 and -5, are multiplied by to get the corresponding y-values, 15 and -15.
As we can see, if we multiply each of the x-values by 3, it will give us their corresponding y-values.
a 2-liter bottle is filled completely with water from a faucet in 10 seconds. how much water is filled in to the bottles each second?
Answer:
[tex]\dfrac{1}{5}\ L[/tex]
Step-by-step explanation:
It is given that,
A 2-liter bottle is filled completely with water from a faucet in 10 seconds.
We need to find how much water us filled in to the bottles each seconds.
In 10 s = 2 L bottle is filled
In 1 s, [tex]\dfrac{2}{10}\ L=\dfrac{1}{5}\ L[/tex] of water is filled into the bottles.
x-4y=8 in slope-intercept form
Answer:
y= 1 over 4 x -2
Step-by-step explanation:
hope you understand that
Answer:
y = [tex]\frac{1}{4}[/tex] x - 2
Step-by-step explanation:
y = mx + b is slope-intercept form of linear equation.
Solve x - 4y = 8 for "y"
- 4y = - x + 8
y = [tex]\frac{1}{4}[/tex] x - 2
What figure will result when the triangle is rotated around RE?
Answer:
The figure will result is cone ⇒ B
Step-by-step explanation:
When a right triangle is rotated about its vertical leg 360°, then it formed a cone its radius is the horizontal leg of the triangle and its height is the vertical lege of the triangle
In the given figure
∵ Triangle TRE is a right triangle
∴ The horizontal leg is RE
∴ The vertical leg is TR
∵ The triangle is rotated around the horizontal leg RE 360°
∴ It formed a cone its radius = TR and its height = RE
∴ The figure will result is the cone
express 182 as a product of its prime factors
Answer:
2x7x13
Step-by-step explanation:
182 = 91 x 2
91 = 13 x 7
5)
2x + 8+ = 32
Solve the question
Answer:
x = 12
General Formulas and Concepts:
Order of Operations: BPEMDAS
Step-by-step explanation:
Step 1: Define equation
2x + 8 = 32
Step 2: Solve for x
Subtract 8 on both sides: 2x = 24Divide 2 on both sides: x = 12Step 3: Check
Plug in x to verify it's a solution.
Substitute: 2(12) + 8 = 32Multiply: 24 + 8 = 32Add: 32 = 32please help me. solve for X
Answer:
1. x = 16
2. x = 17
Step-by-step explanation:
1. The sum of the exterior angles of any polygon is 360 degrees. So, to find x, we can add up all of the angle measures and set them equal to 360, then solve for x:
46 + 93 + 47 + 4x + 62 + 3x = 360
Combine like terms:
248 + 7x = 360
Subtract 248 from both sides of the equation to isolate 7x:
7x = 112
Divide both sides by 7 to find the value of x:
x = 16
2. The sum of the interior angles for a 5-sided polygon is 540 degrees. So, to find x, we can add up all of the angle measures and set them equal to 540, and then solve for x:
5x + 139 + 9x + 71 + 92 = 540
Combine like terms:
14x + 302 = 540
Subtract 302 from both sides to isolate the 14x:
14x = 238
Divide both sides by 14 to find the value of x:
x = 17
I hope this helps :)
Help plss (find the perimeter) thx
Answer:
64 units
Step-by-step explanation:
divide the shape into two shapes:
first one: 15+15+4+4=38
second shape:7+7+6+6=26
pweimwter for the whole shape: 38+26=64 units
EASY MATH QUESTION HELP! Which pair of angles are vertical angles in the picture below?
What are the interior angles in the picture below?
Answer:
B, 3 and 5
Step-by-step explanation:
Answer:
3 and 5 for number 1, 1,4,5 and 8 for number 2
Step-by-step explanation:
5x2 + 4x = 3(2 - x)
help me :p
Answer:
Step-by-step explanation:
5x^2+4x=3(2-x)
5x^2+4x=6-3x
5x^2+4x+3x-6=0
5x^2+7x-6
(5x^2-3x)+(10x-6)
x(5x-3)+2(5x-3)
(5x-3)(x+2)
x=3/5,-2
Square PQRS is transformed as shown on the graph.
Which rule describes the transformation?
Ra 90°
Ro, 180°
O RO, 270
O Ro 360
S
The rule that describes this transformation is R₀ 270°
TransformationTransformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
If a point A(x, y) is rotated clockwise by 270 degrees, the new point is at A'(-y, x)
Quadrilateral PQRS is at P(-3, 5), Q(-1, 3), R(-3, 1) and S(-5, 3). If PQRS is rotated 270 degrees clockwise, the new point is at P'(-5, -3), Q'(-3, -1), R'(-1, -3) and S'(-3, 5)
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